# Expected Utility and Private Islands: How To Gamble

One of the meta things I’m most interested in at this conference is how a bunch of super-smart people with strong understanding of statistics handle coming to Las Vegas. Do we gamble, because we thing we’re smarter than the dealer? Do we avoid it, because we know the expected return from slot machines is something like 90 cents on the dollar?

Years ago, I heard an economist talk about how to play the lottery. I’d like to recount that argument, because I think it’s relevant here, and reinforces the difference between value and utility. Plus, I get to drop a photo of an island into my blog post.

Should you play the lottery? Arguably you shouldn’t play scratch-off games. Typically, these cost like \$1 each, and you might win \$5000 or \$10000. Statistically, the expected value is often something like 50 cents on the dollar, as there’s a good chance you’ll win a little bit fairly frequently. But, the best case is that you, at some point in your life, might win \$5000. Nice, might get you a vacation on that island, but it’s not going to change your life appreciable.

What about MegaMillions-style games, where you give 6 numbers and have astronomically low chances of winning anything? As before, the most likely outcome is that if you buy one \$1 ticket per week, you’ll lose 52 dollars. Not a big loss, still. And the expected return, mathematically, is still in that 50 cents per dollar range. But, what if you win? Everything changes! You can quit your job, buy that private island, and live a life of contentment until the end of your days. Your expected return is similar, but the variance and maximum of the return distribution are vastly higher. And in particular, your best-case utility (your personal mapping of dollars to happiness) goes from minimal change to an enormous, lifestyle-changing impact.

So, if you have to make a choice between playing scratch-off games, or buying lottery tickets, the answer for an economist is clear. Buy lottery tickets, expect to lose, but have fun dreaming about your private island.

And when in Vegas, what should you play? Well, don’t play roulette — it has 35 to 1 odds. I don’t know about you, but I don’t want to put \$10K down to have a 35 to 1 shot at \$350K — the expected utility of most likely losing \$10K is way too high, and the upside is not nearly enough to buy an island. You might be able to do a bit better with sports betting, where 100 to 1 odds certainly exist. But for the big payout, there are a few slot machines that simulate the odds of playing the lottery. The Megabucks machine has odds of 1 in 49,836,032, and you could win \$10 million. Clearly, the expected value is garbage, but still, you could win enough to ditch this conference and buy a (small) island. So that’s what I recommend you do.

If you do win, you’re taking me to dinner at Nobu. Find me at @harlanh on Twitter.